The term "turbulence" is used for a large variety of dynamical phenomena of fluids in motion whenever the details of the flow appear to be random and average properties are of primary interest. Just as wide ranging are the theoretical methods that have been applied towards a better understanding of fluid turbulence. In this book a number of these methods are described and applied to a broad range of problems from the transition to turbulence to asymptotic turbulence when the inertial part of the spectrum is fully developed. Statistical as well as nonstatistical treatments are presented, but a complete coverage of the subject is not attempted.The book will be of interest to scientists and engineers who wish to familiarize themselves with modern developments in theories of turbulence. The fact that the properties of turbulent fluid flow are addressed from very different points of view makes this volume rather unique among presently available books on turbulence.

Preface.- Intermittency in Turbulence (R. Benzi, L. Biferale).- The Problem of Turbulence and the Manifold of Asymptotic Solutions of the Navier-Stokes Equations (F. H. Busse).- Renormalization Methods Applied to Turbulence Theory (D. Mc Comb).- From Rapid Distorsion Theory to Statistical Closure Theories of Anisotropic Turbulence (C. Cambon).- Engineering Turbulence Models and their Development, with Emphasis on Explicit Algebraic Reynolds Stress Models (A. V. Johansson).- Symmetries and Invariant Solutions of Turbulent Flows and their Implications for Turbulence Modelling (M. Oberlack)